{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AVWXLW2KAGRPCOUKI4DG6DWSKK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bbb71a5278000768fa15a72c1817cd2f5863f682d008be2c33c8f946d220ab06","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-10-08T14:55:18Z","title_canon_sha256":"644783ecf074203ecd63597092144772d876884ba1e955fc000e8d664d00a69a"},"schema_version":"1.0","source":{"id":"1910.03436","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.03436","created_at":"2026-07-05T00:10:46Z"},{"alias_kind":"arxiv_version","alias_value":"1910.03436v1","created_at":"2026-07-05T00:10:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.03436","created_at":"2026-07-05T00:10:46Z"},{"alias_kind":"pith_short_12","alias_value":"AVWXLW2KAGRP","created_at":"2026-07-05T00:10:46Z"},{"alias_kind":"pith_short_16","alias_value":"AVWXLW2KAGRPCOUK","created_at":"2026-07-05T00:10:46Z"},{"alias_kind":"pith_short_8","alias_value":"AVWXLW2K","created_at":"2026-07-05T00:10:46Z"}],"graph_snapshots":[{"event_id":"sha256:542a08961aafe6cd6cbcdfd07705b539dfd9b50455916fc020f9a84e75e744a8","target":"graph","created_at":"2026-07-05T00:10:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1910.03436/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we consider the Shigesada-Kawasaki-Teramoto (SKT) model to account for stable inhomogeneous steady states exhibiting spatial segregation, which describe a situation of coexistence of two competing species. We provide a deeper understanding on the conditions required on both the cross-diffusion and the reaction coefficients for non-homogeneous steady states to exist, by combining a detailed linearized analysis with advanced numerical bifurcation methods via the continuation software pde2path. We report some numerical experiments suggesting that, when cross-diffusion is taken into ","authors_text":"Christian Kuehn, Cinzia Soresina, Maxime Breden","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-10-08T14:55:18Z","title":"On the influence of cross-diffusion in pattern formation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.03436","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:aa65a403b78ffca14727e4a7071afc5eeeb9988220f6cd33ec7eb61313e46f91","target":"record","created_at":"2026-07-05T00:10:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bbb71a5278000768fa15a72c1817cd2f5863f682d008be2c33c8f946d220ab06","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-10-08T14:55:18Z","title_canon_sha256":"644783ecf074203ecd63597092144772d876884ba1e955fc000e8d664d00a69a"},"schema_version":"1.0","source":{"id":"1910.03436","kind":"arxiv","version":1}},"canonical_sha256":"056d75db4a01a2f13a8a47066f0ed2529323936eaa7974d10ac7d49c81954209","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"056d75db4a01a2f13a8a47066f0ed2529323936eaa7974d10ac7d49c81954209","first_computed_at":"2026-07-05T00:10:46.627302Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:10:46.627302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"scu8OdEqYWHb9rKgPBLJK8FSQlNzhILR0JmVGdadYVyZYlq4hXWt3lBvThpf/1VjcVfmcAyNYt1ZtxazdVRiDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:10:46.627653Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.03436","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa65a403b78ffca14727e4a7071afc5eeeb9988220f6cd33ec7eb61313e46f91","sha256:542a08961aafe6cd6cbcdfd07705b539dfd9b50455916fc020f9a84e75e744a8"],"state_sha256":"4d7f5c8e81e26364dda94d3dd844bd6163d6d2225e0f31c341e073033388f844"}